six_cubed
plain-language theorem explainer
The equality 6 cubed equals 216 anchors the numerical value of the 3-cube face count in spatial dimension 3. Cross-domain researchers in Recognition Science cite it when confirming that the enumeration 6 appears uniformly across quarks, leptons, cortical layers, Braak stages, and robotic degrees of freedom. The proof is a one-line decision procedure that evaluates the arithmetic directly.
Claim. $6^3 = 216$
background
The module states that the 3-cube has Euler characteristic V - E + F = 8 - 12 + 6 = 2, so the face count is 6. This count is asserted to recur across domains as the face-level enumeration for D = 3, with explicit instances given for 6 quarks, 6 leptons, 6 cortical layers, 6 Braak stages, and 6 robotic degrees of freedom. The local setting is the structural claim that 6 = 2 · 3 where the factor 2 is the binary-state count of a face.
proof idea
The proof is a one-line wrapper that applies the decide tactic to the decidable equality on natural numbers.
why it matters
This theorem supplies the concrete value 216 that appears in the CubeFaceUniversalityCert structure aggregating the six-count certificates for Quark, Lepton, CorticalLayer, BraakStage, and RoboticDOF. It fills the numerical step in the cube-face universality claim for D = 3, consistent with the spatial-dimension forcing T8 in the Recognition Science chain. No open questions are attached.
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